Method for stress assessment that removes temperature effects and hysteresis on the material property measurements

ABSTRACT

An apparatus for the nondestructive measurement of materials that includes at least two layers of electrical conductors. Within each layer, a meandering primary winding is used to create a magnetic field for interrogating a test material while sense elements or conducting loops within each meander provide a directional measurement of the test material condition. In successive layers extended portions of the meanders are rotated so that the sense elements provide material condition in different orientations without requiring movement of the test circuit or apparatus. Multidirectional permeability measurements are used to assess the stress or torque on a component. These measurements are combined in a manner that removes temperature effects and hysteresis on the property measurements. This can be accomplished through a correction factor that accounts for the temperature dependence.

RELATED APPLICATIONS

This application is a divisional of U.S. application Ser. No.12/157,719, filed Jun. 12, 2008, now U.S. Pat. No. 8,222,897, whichclaims the benefit of U.S. Provisional Application Nos. 60/934,191 filedJun. 12, 2007, 60/999,126 filed Oct. 16, 2007, 61/070,654 filed Mar. 25,2008, and 61/125,860 filed Apr. 29, 2008.

The entire teachings of the above applications are incorporated hereinby reference.

GOVERNMENT SUPPORT

The invention was supported, in whole or in part, under contractW911W6-08-C-0006, from the U.S. Army. The Government has certain rightsin the invention.

BACKGROUND OF THE INVENTION

The technical field of this invention is that of nondestructiveevaluation for material characterization, which includes quantitative,model-based assessment of surface, near-surface, and bulk materialcondition for flat and curved parts or components. Characterization ofbulk material condition includes measurement of changes in materialstate such as degradation or damage, assessment of residual stresses andapplied loads, and assessment of processing-related conditions, forexample, from shot peening, roll burnishing, or heat treatment. It alsoincludes measurements characterizing the material, such as alloy type,and material states, such as porosity and temperature. Characterizationof surface and near-surface conditions includes measurements of surfaceroughness, changes in relative position, coating thickness, and coatingcondition. Each of these includes detection of variations inelectromagnetic sensor responses associated with the presence of flawconditions or microstructural, compositional, or magnetic structure(e.g., domain orientation) changes.

A particular aspect of this invention is related to sensing andmonitoring mechanical stress, strain, and load on a material. Stress andload monitoring are important for developing health usage and monitoringsystems for vehicles such as rotorcraft. These systems requiretechnologies such as direct load monitoring, on-board damage monitoringand advanced diagnostics for early fault detection to meet the demandfor increased safety and reduced operational cost. For example, earlydetection of damage and cracks in air vehicle structures supports a moreeffective damage tolerance approach and supplements mechanicaldiagnostics and usage monitoring. In particular, on-board damagemonitoring can provide timely detection of mechanical damages thatremain undetectable by conventional methods until the next scheduledinspection, which can enhance safety, improve readiness and missionperformance, and reduce maintenance costs. The fields of strain sensing,using strain gages, and load monitoring are relatively mature withnumerous approaches that enable monitoring of stresses, strains andloads. These include conventional strain gages, optical fiber straingages, and ultrasonic methods.

Magnetic field or eddy current sensors have also been used to assessstress on a material. Conventional eddy-current sensing involves theexcitation of a conducting winding, the primary, with an electriccurrent source of prescribed frequency. This produces a time-varyingmagnetic field, which in turn is detected with a sensing winding, thesecondary. The spatial distribution of the magnetic field and the fieldmeasured by the secondary is influenced by the proximity, physicalproperties (electrical conductivity and magnetic permeability), andgeometry (layer thickness) of nearby materials. When the sensor isintentionally placed in close proximity to a test material, the physicalproperties of the material can be deduced from measurements of theimpedance between the primary and secondary windings. As an example,Goldfine et al. have disclosed methods under U.S. Pat. Nos. 5,015,951,RE36,986, 5,453,689, 5,793,206, 6,188,218, 6,252,398, 6,377,039, and6,657,429 that describe magnetic field sensors that operate in themagnetoquasistatic regime (in other words, the wavelength of travelingwaves is long compared to the sensor dimensions). These sensors useprecomputed databases of sensor response to estimate the lift-off(sensor proximity) and directional magnetic permeability, directionalelectrical conductivity, and layer thicknesses for uniform, layered andmodified-surface materials. As another example, U.S. Pat. No. 5,828,211to Scruby et al. describes measuring a response of a directionalmagnetic field sensor as the sensor is rotated over a test material andusing this information to determine the biaxial stress distribution.

SUMMARY OF THE INVENTION

Aspects of the methods described herein involve test circuits for thenondestructive evaluation of electrical properties of materials and theuse of these properties to assess material conditions of interest, suchas load related parameters, or stress in vehicular drive trains andsimilar mechanisms, such as those used in rotorcraft.

In one embodiment, a test circuit has at least two layers of primarywinding electrical conductors to impose a magnetic field or flux in atest material when driven by an electric current. These conductorsfollow a meandering path and have segments with linear parallel extendedportions and cross-connections at the ends of the segments. The extendedportions in each layer are positioned at an angle with respect to theextended portions in each other layer. In addition, the test circuit hasat least one sense element associated with each primary winding, wherethe sense element has conducting segments aligned with the extendedportions of the primary winding to link magnetic flux from the primarywinding. Each sense element also has a feature, such as a length orposition with respect to each non-associated primary winding, which canbe selected to minimize the flux from the non-associated primarywinding. This allows each sense element to be sensitive only to theproperties of the test material in a direction corresponding to theassociated primary winding and this allows the test circuit to monitormultiple material property directions without having to move the testcircuit with respect to the test material.

The sense elements can be configured in a variety of ways. In oneembodiment, the sense element feature used to minimize the flux fromnon-associated primary windings is the position of the center of thesense element, and the sense element is centered over a conductingsegment of a non-associated primary winding. In another embodiment, thefeature is sense element length, and the length is an integral multipleof twice the distance between extended portions of a non-associatedprimary winding divided by the sine of the angle between extendedportions of the non-associated and associated windings. In anotherembodiment, the sense elements are centered between the extendedportions of the associated primary winding. The sense elements may be inthe same layer or a different layer as the associated primary winding.

The term “direction” in this document means a set of parallel lines in atwo-dimensional plane (the surface of the material). One such set willbe chosen as the 0° direction, and other sets (directions) will beidentified by the angle between lines in those sets and lines in the 0°direction. Since there is no polarity to the direction (these are lines,not rays), directions whose angles differ by 180° are the same, e.g.,the −45° direction is the same as the 135° direction, −60° is the sameas 120°, etc.

For measurements in two directions, the angle between extended portionsof the primary windings in two different layers is 90°. Furthermore,when this pair of primary windings is driven in series, the net dipolemoment for the combination is zero. In another embodiment, the testcircuit permits measurements in four directions. In a particularembodiment, the relative directions between the extended portions are0°, 45°, 90°, and −45° (135°). The test circuit can be operated as fourindividual primary windings, or two pairs of primary windings, which mayalso be connected in series. Inter-layer connections between the ends ofthe segments of the primary windings in some layers may also be present.

This directional test circuit can be used to assess directionalproperties and condition of a test material. In one embodiment, the testcircuit is used to obtain a stress-dependent property in each direction,a stress-independent property, and another feature of interest, such asthe sensor proximity to the test material surface. The test circuitallows electrical properties of the material to be measured at multipleorientations without having to move the sensor. In an application, suchas a measurement of a magnetizable steel component, the magneticpermeability, electrical conductivity, and lift-off (distance betweensensor and component) are measured for each sense element orientation.This then allows load-related parameters to be determined in eachorientation, such as torque, bending load, axial load, temperature,vibration, or rotational speed. Since the measurements are performedwith the same nominal lift-off between the test circuit and the surfaceof the material being examined, and the distances between layers in thestacked construct are known, the measurement of the lift-off with eachsense element orientation provides redundancy and the capability formeasurement consistency validation. Alternatively, the independentinformation provided by the multiple sensing elements can be used toincrease the number of unknowns that can be estimated independently. Forexample, for a four-direction sensor, it is possible to measure thestress-dependent magnetic permeability in each direction, while theelectrical conductivity is stress-independent. The measurements of theelectrical conductivity can be used to correct for variations inenvironmental factors such as temperature.

In an embodiment, the stress or load on a test material is assessed byplacing a sensor proximate to the test material with the sensorproviding drive windings and sense elements that permit measurements ofa magnetic permeability, in at least two different directions. The senseelements predominantly couple to one of the drive windings and not tothe others and permit monitoring of an overlapping area between thevarious drive windings and sense elements. The magnetic permeabilityobtained with each sense element typically exhibits hysteresis as theapplied load is varied, but correction and compensation for thishysteresis in a specific or first direction can be accomplished by usingthe magnetic permeability information from a second direction. Inparticular, by loading the test material to a known level, a correctionfactor can be computed that will remove the hysteresis from the magneticpermeability measured for the first direction, which in turn can becorrelated with the stress in the first direction. While not required,it is often convenient to measure the responses from each sense elementsimultaneously.

In a specific embodiment, the test material is a rotating cylinder orshaft, the sensor has two pairs of orthogonal drive winding and senseelements, and the sensor is located in a stationary position, not incontact with the cylinder. This then allows for a non-contactmeasurement of the stress on the rotating cylinder. Example measuredloads are the torque, axial load, and bending loads on the cylinder. Inaddition, the cylinder can be a spinning shaft as part of a drive systemand the cylinder may be a ferrous metal element such as a magnetizablesteel.

Another embodiment describes an approach that generates a linearrelationship between a measured magnetic property, such as magneticpermeability, and a material stress. This requires correcting forhysteresis and temperature dependent material property variations, buthas distinct advantages in control system applications where a linearresponse is often required for efficient system operation. The linearresponse is obtained by disposing at least two magnetic sensors near atest material surface with each sensor providing a directionalmeasurement of a magnetic property as a load applied to the testmaterial is varied. The uncorrected magnetic property in a firstdirection or a direction of interest typically varies nonlinearly withstress and exhibits hysteresis. Combining this response with acorrection factor results in a corrected magnetic property value, thisexhibits substantially less hysteresis and a linear variation withstress. The correction factor is determined by comparing the magneticproperty values in the first and additional directions for at least twoknown levels of applied loads. In particular, the correction factor canuse the magnetic property in a direction experiencing a known appliedload to normalize the magnetic property value in the first direction toremove the effect of temperature.

In specific embodiments, the corrected magnetic property values are usedas inputs to a control algorithm, for adjustment of loads duringassembly operations, to monitor a process on a material, or for coatinga substrate with another material layer. The approach can also be usedfor heterogeneous materials, such as composite structures, where thecorrected magnetic property represents the real part of a diamagneticcomplex permeability representation for the test material.

In yet another embodiment, composite materials can be assessed usingthese methods to provide, for example, applied load or temperature. Manycomposites contain a woven fiber or fabric material embedded within amatrix material. The condition of the composite, such as a graphitefiber/epoxy composite, can be determined from magnetic sensormeasurements of the composite response. In particular, for a directionalmagnetic sensor geometry, the drive windings and sense elements of thesensor can be aligned with the fibers inside the composite to enhancethe sensitivity of the measurement. Furthermore, with sensors thatprovide directional sensitivity in at least two directions, theorientation angle between the fields generated by the distinct drivewindings can be selected to match the angles of between the fiberdirections in the composite. If necessary, the bulk properties of thecomposite can be modeled as a complex diamagnetic permeability and thecomponents of the complex permeability, such as the real and imaginaryparts or equivalently the magnitude and phase, can be related tocomposite condition.

Another aspect of this invention is that the relative motion between thesensor and the test material can influence the sensor response. Toassess the stress on a rotating cylinder, since the depth of penetrationof the sensing magnetic field and sensor response can change with therotation rate of the cylinder, the sensor is operated with an excitationfrequency above a predetermined level where depth of penetration doesnot vary significantly with rotation rate. In addition, the sensor iscalibrated by combining at least two load conditions and two differentlift-offs or sensor proximities during the initial installation of thesensors. During operation a response is measured for each sense elementand used to estimate the stress on the cylinder. This typically involvesa correction for temperature variations in the sensor response. Forexample, the temperature correction can be accomplished by estimatingthe stress in a direction with approximately constant loading anddetermining a correction factor that can be applied to the data in otherdirections where the loading is not constant. Alternatively, usingdatabases of precomputed responses permits independent estimation of theconductivity and permeability of the test material. The conductivityresponse can be used to assess the temperature variations and used tocorrect the measured magnetic permeability, which in turn is correlatedwith the stress. The stress estimation signal-to-noise ratio can also beimproved by using spatially sequence averaging where data obtained overmultiple cylinder rotations is averaged based on the rotation position.The signal integrity can be further enhanced by using responses fromsensors placed at different circumferential positions. A coating may beadded to the cylinder to enhance sensitivity to the stress measurement.The sensor can also be attached to the cylinder with electricalconnections to the sensor leads made through slip rings.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, features and advantages of theinvention will be apparent from the following more particulardescription of preferred embodiments of the invention, as illustrated inthe accompanying drawings. In the drawings like reference charactersrefer to the same parts throughout the different views. The drawings arenot necessarily to scale, emphasis instead being placed uponillustrating the principles of the invention.

FIG. 1 shows an expanded view drawing of a bidirectional MWM havingprimary windings in two layers;

FIG. 2 shows a top view drawing of a bidirectional MWM having primarywindings in two layers;

FIG. 3 shows an expanded view drawing of a quadridirectional MWM havingprimary windings in four layers;

FIG. 4 shows a top view drawing of a quadridirectional MWM havingprimary windings in four layers;

FIG. 5 shows a top view drawing of an array having threequadridirectional MWM sensors;

FIGS. 6 and 6A shows a schematic drawing for a full three-dimensionalstress state;

FIG. 7 shows a schematic drawing for a two-dimensional surface stressstate;

FIG. 8 shows a schematic drawing for a pure tension loading mode for acylindrical shaft;

FIG. 9 shows a schematic drawing for a pure torsion loading mode for acylindrical shaft;

FIG. 10 shows a schematic drawing for a pure bending loading mode for acylindrical shaft;

FIG. 11 shows a representative measurement grid relating the magnitudeand phase of the sensor terminal impedance to the lift-off and magneticpermeability;

FIG. 12 shows a representative measurement grid relating the magnitudeand phase of the sensor terminal impedance to the lift-off andelectrical conductivity;

FIG. 13 shows the magnetic permeability variation with bending stress ina shot-peened high-strength steel specimen.

FIG. 14 shows a cross-sectional view of a cylindrical sleeve and sensorinserts for non-contact torque monitoring of a rotating shaft.

FIG. 15 shows a top view of a cylindrical sleeve and sensor inserts fornon-contact torque monitoring of a rotating shaft.

FIG. 16 shows a cross-sectional view of a cylindrical sleeve and sensorsplaced around an offset, rotating shaft.

FIG. 17 shows the magnetic permeability variation with increasing stressfor a quadridirectional sensor in one orientation.

FIG. 18 shows the lift-off corresponding to the measurement of FIG. 17.

FIG. 19 shows the magnetic permeability variation with increasing stressfor a quadridirectional sensor oriented at −45° with respect to thesensor in FIG. 17.

FIG. 20 shows the lift-off corresponding to the measurement of FIG. 19.

FIG. 21 shows the magnetic permeability variation with increasing torquefor a quadridirectional sensor mounted on a steel cylinder.

FIG. 22 shows the lift-off corresponding to the measurement of FIG. 21.

FIG. 23 shows the permeability versus stress at 0° and 90° over twostress range cycles at room temperature (68° F.).

FIG. 24 shows the permeability versus stress after application ofhysteresis correction.

FIG. 25 shows the permeability versus stress at various temperatures.

FIG. 26 provides a flow diagram that illustrates the process forconverting a QD-MSG response into a non-contact load measurement.

FIG. 27 shows a plot of the corrected QD-MSG response versus stress(derived from the strain gages) caused by multi-axial loading and usingthe static test setup.

FIG. 28 shows a plot of the temperature dependent QD-MSG response versusstress caused by multi-axial loading and using the static test setup.

FIG. 29 shows the permeability response in the four directions of aQD-MSG before hysteresis correction, but after temperature correction.

FIG. 30 shows a plot of the QD-MSG measured torque versus appliedtorque, after temperature and hysteresis corrections, for thecalibration ramp.

FIG. 31 shows the QD-MSG-measured lift-off (displacement from theaverage) as a function of circumferential angle, for intended “puretorque” and bending loads.

FIG. 32 shows the effect of calibration procedure on hysteresiscorrection where an initial calibration procedure was used.

FIG. 33 shows the effect of calibration procedure on hysteresiscorrection using a calibration procedure refined after the seconddynamic test.

FIG. 34 shows torque estimates based on the QD-MSG's versus the torqueestimated based on strain gages. Several of the data sets includebending loads.

FIG. 35 shows the correlation of the MWM sensor network torque estimatewith reported mean engine torque.

FIG. 36 shows a schematic diagram for a composite structure with amagnetic field sensor placed over the material surface.

FIG. 37 shows a plot of the depth of penetration of a spatially periodicmagnetic field into a test material as the convection velocity orrotation rate is varied.

DETAILED DESCRIPTION OF THE INVENTION

A description of preferred embodiments of the invention follows.

This invention addresses the need for apparatus and methods for improvednondestructive assessment of material condition, particularly insituations where the material condition is anisotropic, i.e., it dependsupon direction. Representative applications include measurements ofresidual stress, axial load, bending load, and torque. This isaccomplished using sensor or test circuit constructs that use magneticfields to interrogate a test material and do not require rotation of theconstruct to provide directional property information. The sensors aremounted near or onto a test material surface and are operated in thequasistatic frequency regime. In particular, sensor or test circuitconstructs are described which allow the material condition to bedetermined through electrical property measurements at multipleorientations without having to move the sensor.

FIG. 1 shows an expanded view of a bidirectional meandering windingmagnetometer (MWM®) sensor. This sensor geometry is based upondirectional MWM, which is planar, conformable eddy-current sensor thatwas designed to support quantitative and autonomous data interpretationmethods and is described, for example, in U.S. Pat. Nos. 5,453,689,5,793,206, 6,188,218, and 6,657,429. In this case, the sensor has twolayers (16 and 18) of conducting segments. Each layer has a primarywinding 14 having meandering conducting segments and extended portions10 for creating a magnetic field. Each layer also has sense elements orsecondary windings 12 parallel to and centered between adjacent extendedportions of the primary winding for sensing the response. In this casean inter-layer conductor or via 20 at the end of the segments for eachlayer allows current to flow between the primary winding conductingsegments in pairs of layers. If separate connections are made to theprimary windings in each layer, then vias are not required, and eachlayer can be excited individually. The primary winding is fabricated ina spatially periodic pattern with the dimension of the spatialperiodicity termed the spatial wavelength λ. The layers are then stackedto create the relatively thin and flexible sensor construct 8 shown inFIG. 1 and FIG. 2. Each sensing element has separate connection leads24, which allows each sense element to have a separate outputconnection; alternatively, a common output connection can be used forthe sense elements associated with the same primary winding, typicallyin a single layer, by appropriately cross-connecting the connectionleads 34 in series.

A current is applied to the primary winding 14 to create a magneticfield and the response of the test material to the magnetic field ismeasured through the voltage at the terminals of the secondary windings.This voltage reflects the condition of the test material and isdependent upon the orientation of the sensor, such as the extendedportions of the drive winding, with respect to any directional propertyvariations in the test material. This sensor is capable of independentdirectional measurement of permeability, conductivity, or otherproperties. This makes it useful, for example, in applications thatrequire measurement of stress (residual or applied), including thevarious stresses experienced by a shaft under torsional, bending, andaxial loads. With the extended portions in one layer (10) rotated or anangle with respect to the orientation of the extended portions inanother layer (30), the sensor can respond to material propertyvariations in two directions without having to move or rotate the sensoragainst the test material surface. Each sense element provides anindependent measurement of the lift-off, which is the proximity betweenthe sensor and the surface of the material being examined. Since themeasurements are performed with the same nominal lift-off, accountingfor the distances between the stacked layers, this redundancy permitsthe consistency of the measurement to be verified or validated. Forexample, when using a measurement grid as described below, each of thedata points, which correspond to data from sensing elements in differentlayers, should map out a lift-off line when examining a material withuniform properties. Alternatively, the simultaneous measurement of eachsense element at same location provides independent information thatallows more unknowns to be determined; since the difference in lift-offbetween sensing elements is known, the measurement information fromdifferent sense elements can be used to determine an electrical orgeometric property of the test material instead of using thatinformation to determine the lift-off for each individual sense element.

The sensor in FIG. 1 has orthogonal primary windings 14 and permitsmeasurements at 0° and 90°. The primary windings are designed so thatthe short side element 32 of the primary in each layer partiallycompletes an additional period of the primary winding in the otherlayer. In this sense the primary windings in these layers are paired andwhen driven in series the fields from the primary windings arecomplementary. In this layout, the primary winding pair has no netdipole moment, which eliminates the need for double-loop primary layoutsdescribed, for example, in U.S. Pat. No. 6,657,429. The secondaryelements are insensitive to the magnetic fields of theperpendicular-orientation windings because the net magnetic flux thatthey link cancels out to zero, which, in this embodiment, is due to thesecondary elements being positioned symmetrically across a long segmentof the non-associated primary winding, as discussed in more detailbelow. This flux cancellation will only happen if the material undertest is uniform across the sensor footprint; the secondary elements willhave some sensitivity to property gradients in the perpendicularorientation.

An important feature of this directional sensor design is the senseelements are configured to be sensitive to one associated set of primarywinding conductors or the associated primary winding of a single layer.Features of the sense element, such as the sense element position andsize, are adjusted to minimize and ideally eliminate the magnetic fluxfrom the non-associated primary windings in other layers so that thesense elements are insensitive to the flux linked from these otherprimary windings. One mechanism for minimizing this flux is to make thecenter point of the sense element loop lie over the long segment of anon-associated primary winding. This symmetry allows the flux to becancelled for any sense element length and orientation angle. A secondmechanism for minimizing the flux from non-associated primary windingsis to choose the length of the sense element appropriately. A secondaryelement will be insensitive to a primary winding that is at angle α withrespect to the sensing element, as long as the sense element length isan integral multiple of l=λ/sin(α), where λ is the spatial wavelength ofthe primary winding (defined as twice the distance between adjacent longsegments), since this length (l) is the periodicity of the magneticfield generated by the primary at the angle of the secondary. Any sensorconfiguration with two or more primaries where the sense elements arelaid out so as to be insensitive to the magnetic fields generated by allnon-associated primary winding, using either of these two mechanisms,will constitute a multi-directional sensor.

FIG. 3 shows the layout of a quadridirectional MWM sensor capable ofsimultaneous independent measurement in four directions. For stressmeasurements, this sensor is also referred to as a quadridirectionalmagnetic stress gage (QD-MSG). These directions are designated by 0°,90°, −45°, and 45° which are chosen to align with the directions thatthe magnetic permeability would be measured for a magnetizable material.In this example construct, two pairs of complementary layers arecombined to form two bidirectional sensors (40 and 42) which are thenstacked to form the quadridirectional sensor 44. The extended portionsbetween each pair are rotated, in this case by 45°, in order to provideadditional directional sensitivity. The traces or conducting segmentsfor each pair are fabricated onto different layers, for example layers36 and 38 correspond to bidirectional sensor 42 while layers 16 and 18correspond to bidirectional sensor 40. The 0/90° and −45/45° orientationprimary windings can be driven simultaneously in series orindependently. FIG. 4 shows a top view of the sensor conductors when thelayers are stacked. In the design of the quadridirectional sensor shownin FIG. 3, the secondary elements' length is set to l=λ√2, making theminsensitive to primary windings at both 45° and −45°, and they arecentered in a way that makes them insensitive to primary windings at90°. Note that −45° and 45° are the only angles that would allowsecondary elements to be insensitive to both 0° and 90° primarywindings. In the discussion associated with the quadridirectional sensorof FIG. 3, it was convenient to describe the operation in terms ofstacked pairs of bidirectional sensors. However, the directions andorientations of the primary windings for each layer can be in any order.Adjacent layers are not required to be at 90° angles with respect toeach other.

Clearly, variations on the test circuit designs are possible based onthe described approach. For example, it is preferred to have the senseelements in the same layer as the primary winding associated with thesense element. Alternatively, the sense elements may be placed on otherlayers and without primary winding conductors if desired. However, thisincreases the thickness of the sensor and can reduce its flexibility forconforming to material surface. Also, other sensor configurations canalso be used as long as one of the flux canceling mechanisms describedabove is used. For example, a tridirectional sensor could have primarywindings oriented at angles of 0°, 60° and −60° (120°) with a senseelement length of l=2λ/√3. Furthermore, a variety of connections can bemade to the sense elements. For example, for the drive winding orientedto provide sensitivity in the axial direction, individual connectionscan be made to each of the sense elements to improve the spatialresolution of the measurements. Cross-connecting the sense elements thenprovides a single output for each of the other orientations so thatseven measurement channels are used. This can simplify theinstrumentation and permits a combination of temperature, stress, andproximity measurements at the same time.

One application for this multi-directional sensor is the measurement oftorque on a rotating shaft. Torque in a shaft results in stressesoriented at ±45° from the axial direction. Thus the magneticpermeability, which is a strong function of stress for ferromagneticmaterials such as steels, should be measured in these two directions inorder to determine the torque. However, stresses may also be present dueto axial and bending loads. Permeability data from all four directions(0°, 90°, −45°, and 45°) at multiple circumferential locations can beused to independently measure these various stresses, and it can also beused to minimize the measurement's unwanted dependence on materialproperty variations in the shaft, hysteresis in the permeability/stressrelationship, temperature, vibration, etc. The array format of FIG. 5,which illustrates three quadridirectional MWM sensors 44 fabricated ontoa common substrate as a sensor array 46, allows three locations to bemonitored simultaneously. Adjacent quadridirectional sensors may beoriented at 45° with respect to each other so that if only one set ofprimaries is driven then the directions of sensitivity for the sensorswill alternate. Depending upon the size of the shaft, additional orlonger arrays can be used. For example, if three arrays are required toprovide coverage around the circumference, this results in 9 locations.At each location the properties are measured in four directions, whichresults in a total of 36 measurement channels. Two-dimensional arrays ofsuch sensors could also be fabricated. These sensor palettes could bemounted on a flexible substrate and used to monitor material properties,such as temperatures and stresses, over wide areas, for example, onbridge members and pipelines, and on the opposite surface of a materialduring machining, during shot peening or forming, to monitor residualstresses.

In operation, the multi-directional sensors can be embedded betweenmaterial layers or behind a part being processed in order to monitor thematerial properties and material condition during processing. Thesensors could be used to measure properties in multiple directionssimultaneously during processing and these properties could be usedmonitor the quality of the process and could even be used as inputs fora controller to control the process. Example processing operationsinclude those which add material or change material properties on thesurface, such as shot peening, friction stir welding, laser shockpeening, coating, heat treating, forming, machining, and milling.Example material properties include magnetic permeability, electricalconductivity, and dielectric permittivity while example materialconditions of interest for process control include strength,temperature, stress, and velocity. Similarly, the sensor could beembedded within a device that controls another device as part of theprocess control. To understand the stress components better, considerthe geometry of FIGS. 6 and 6A. In a generic stress state there are sixcomponents of stress. Three of these components are normal stresses andthree are shear stresses. Since the magnetic field sensors describedabove monitor the material through the surface, three of these stressesare zero, since there will be no forces acting on the surface. Using thecoordinate system of FIGS. 6 and 6A, these stresses are σ_(YY), τ_(XY),and τ_(YZ). With this constraint, a two-dimensional stress-state issufficient to fully describe the loading. Such a two-dimensionalstress-state is shown in FIG. 7.

In many applications, the net loading on a material or component is thecombined result of multiple loading modes. Assuming a linearly elasticmaterial, multiple loading modes can be added together or superimposedto produce a combined loading state. As a specific example, the loadingmodes to be considered are pure tension, pure torsion, and pure bendingon a cylindrical shaft. The shaft is assumed to be circular and ofconstant cross section since this is the most common geometry used fortorque transmission. This includes both solid and hollow shafts. In puretension, the tension is assumed to be applied in the axial (z) direction(see FIG. 8). It follows that the stress can be expressed as σ_(zz)=P/A,with P the applied axial load (force) and A the cross-sectional area. Inpure torsion, the torsion load is assumed to be applied in the axial (z)direction (see FIG. 9). It follows that the shear stress is only at thesurface of the shaft and can be expressed as τ=TR_(O)/J, with R_(O) theradial distance from the axis, J the polar moment of inertia, and T theapplied torque. In pure bending, it is assumed that only a pure momentis being applied (i.e., no shear) in the XY plane of FIG. 10. Even inthe case of a cantilevered load, the bending stresses are usually muchlarger than shear stresses so the shear stresses can be ignored. Also,shear stresses due to bending must be zero at the surface, furtherminimizing the effect on the surface stress measurement. The result isthat the bending stress can be expressed as σ_(zz)=(R_(O)/I)(M_(X) sinθ−M_(Y) cos θ) with/the moment of inertia and θ the angle between thepoint of interest and the x axis, and M_(X) and M_(Y) are the moments(torques). It follows that the combined loading stress can be obtainedby superposition as σ_(zz)+P/A+(R_(O)/I)(M_(X) sin θ−M_(Y) cos θ) withσ_(zz)=0.

In operation, measurements are made with each sense element to obtain atleast one electrical property and an additional property, where theelectrical property is used to determine a material condition, such asstress and the additional property is used to obtain another feature ofinterest. For example, typical properties obtained from multipleexcitation frequency measurements are the magnetic permeability andelectrical conductivity, which are electrical properties, and lift-offor sensor proximity to the test material surface. This allows materialelectrical properties to be measured at multiple orientations withouthaving to move the sensor. In an application, the magnetic permeability,electrical conductivity, and lift-off are measured for each senseelement orientation. This allows load-related parameters to bedetermined in each orientation, such as torque, bending load, axialload, temperature, vibration, or rotational speed. For comparison, U.S.patent application Ser. No. 11/702,422, filed Feb. 5, 2007, the entireteachings of which are incorporated herein by reference, describes theuse of magnetic field sensors at multiple locations around a rotatingcomponent for assessing the condition of the rotation component, but itdoes not teach of integrated constructs that provide multipleorientation responses within the same sensor footprint. Similarly, U.S.Provisional Application No. 60/934,191, filed Jun. 12, 2007, the entireteachings of which are incorporated herein by reference, describesextending the use of magnetic field sensors to perform non-contacttorque measurements of rotating members.

Also in operation, the excitation of the drive or primary windings ineach layer can be adjusted or selected based upon the propertymeasurement application of interest. In one approach, the excitation ofthe different primary windings can be synchronized to measure couplingeffects between directions for materials that have coupled magneticproperties. The drives can be varied so that primary is excited with aDC signal while the others have AC excitations or all can be excitedwith AC excitations either with different phase shifts, which can createa rotating field direction, or with different excitation frequencies.This could be used, for example, with suspensions of ferromagneticparticles such as ferrofluids, with the excitation frequency and phaseshift adjusted to synchronize the field directions with the fluidmotion.

In another approach the sensing elements are used between differentdrive windings and sense elements to provide sensitivity to othermeasurement modes. For example, for a magnetizable material, hysteresiseffects or even the magnetization (B/H) curve can be traced by excitingone primary winding and measuring a response with one or morenon-associated sense elements. Similarly, a DC bias field could beexcited with one winding and the response measured in the orthogonaldirection. It is also possible to place another drive winding orexcitation coil around a sensor to apply a uniform magnetic field normalto the sensor surface.

The multi-dimensional sensor could be used for testing on a variety ofother applications. Examples include magnetic particle suspensions;electronic materials; laboratory or test tube samples; objectcharacterization and assessment; and implants such as those used indental applications. Typically it is beneficial to convert the senseelement response into more meaningful physical parameters associatedwith the test material, such as an electrical conductivity or magneticpermeability. In addition, if the sensor lift-off or proximity to thetest material is determined, this provides self-diagnostic informationabout the state of the sensor, which is particularly useful forsurface-mounted sensor arrays where access to the sensor array may belimited.

An efficient method for converting the sensor response into material orgeometric properties is to use grid measurement methods. These methodsmap two known values, such as the magnitude and phase or real andimaginary parts of the sensor impedance, into the properties to bedetermined. The measurement grids are two-dimensional databases that canbe visualized as “grids” that relate two measured parameters to twounknowns, such as the magnetic permeability (or electrical conductivity)and lift-off (where lift-off is defined as the proximity of the testmaterial to the plane of the MWM windings). For the characterization ofcoatings or surface layer properties, three-(or more)-dimensionalversions of the measurement grids, called lattices and hyperlattices,respectively, can be used. Alternatively, the surface layer parameterscan be determined from numerical algorithms that minimize the errorbetween the measurements and the predicted responses from the sensor, orby intelligent interpolation search methods within the grids, latticesor hyperlattices.

For ferromagnetic materials, such as many steels, a measurement grid canprovide a conversion of raw data to magnetic permeability and lift-off.A representative measurement grid for ferromagnetic materials isillustrated in FIG. 11. A representative measurement grid for alow-conductivity nonmagnetic alloy (e.g., titanium alloys, somesuperalloys, and austenitic stainless steels) is illustrated in FIG. 12.For coated materials, such as cadmium and cadmium alloys on steels, theproperties of the coatings can be incorporated into the model responsefor the sensor so that the measurement grid accurately reflects, forexample, the permeability variations of substrate material with stressand the lift-off. Lattices and hyperlattices can be used to includevariations in coating properties (thickness, conductivity,permeability), over the imaging region of interest. The variation in thecoating can be corrected for each sensor or sense element individuallyto improve the measurement of permeability in the substrate for thepurpose of assessing stresses. The effective property can also be alayer thickness, which is particularly suitable for coated systems. Forexample, the thickness of paint between the sensor and the surface ofthe material under examination, such as a steel ring gear can be allowedto vary. Since the sensor independently measures the magneticpermeability and lift-off, the measured permeability is effectivelycompensated for the paint thickness variations.

For monitoring the stress on a material, the effective property beingmeasured by the sensor needs to be stress-(or strain)-dependent. Formagnetizable materials, such as steels, this effective property istypically the magnetic permeability. FIG. 13 shows an example magneticpermeability variation with applied stress for a shot-peenedferromagnetic steel at several excitation frequencies. Also, forsensors, such as those shown in FIGS. 1-5, that have the capability toperform directional permeability measurements, the directions of theprincipal stresses can be determined. This orientation dependence canalso affect the sensitivity of the sensor to the dynamic stresses fromthe rotating component. For non-magnetizable materials, the stress-(orstrain)-dependent material property is typically the electricalconductivity. As described for example in U.S. patent application Ser.No. 11/292,146, filed Nov. 30, 2005, the entire teachings of which areincorporated herein by reference, the electrical conductivity ofnumerous metals varies with the applied stress. Both of the abovereferences also describe performing dynamic stress measurements as amaterial is being mechanically loaded. Another option for the monitoringof non-magnetic materials is to add a ferromagnetic coating, such as acobalt- or nickel-based alloy, as a diagnostic layer that can enhancethe observability of the state of the material of interest. Forcomposites or otherwise heterogeneous materials, the effectiveconductivity or effective complex permeability can be used to measurethe stress.

For rotating cylindrical components, the sensors can be mounted aroundthe component in a variety of ways. Typically, even though the componentof interest is rotating, the sensors are kept stationary. For example,the sensors can be mounted in a non-contact configuration where an airgap is intentionally introduced or maintained to avoid direct contactbetween the sensor and the test material. As another example, thesensors are mounted to a ring that encircles the rotating component. Thesensors may be placed around the entire circumference of the ring, oronly at several discrete locations. Then, at each measurement time eachsensor will reflect the interaction between the ring and rotatingcomponent at a specific rotational position. Subsequent measurements aregenerally taken at other rotational positions, since the rotation rateand data acquisition rates are generally not synchronized. The output ofthe sensors can be used to detect a misalignment of the rotating bodythrough its interaction with the ring material, may be used to adjustthe balance, and can even determine if a component is operating withinan acceptable range of stress variation. Note that the sensors can bebonded to the surface using an adhesive or epoxy. Alternatively, thesensors can be mounted on a substrate, routed around a closed loop andtightened without a bonding material to monitor stress or strain, andthen removed without affecting the object under test or requiringsignificant surface preparation.

Similarly, the measurement of the sensor or sense element responses canbe performed in a variety of ways. For example, for magnetic fieldsensors, the drive windings can be series connected so that each sensoris active at the same time. However, if a large number of sensors are tobe monitored, the sensors can be grouped to have a common drive andmonitored by separate electronics modules within each group. Groups ofindividual sense elements within a sensor array may also be connectedtogether to increase the sense area. This reduces the number of senseareas that need to be monitored and permits averaging of the stress orstrain, avoids effects of local property variations, and can improve thesignal-to-noise ratio. Multiplexing between the sense elements or groupsof sense elements enables monitoring of even more sensors for a giveninstrument having a limited number of data acquisition channels, butthis dilutes the ability to monitor all channels simultaneously.

In operation, the sensors can be used for long-term monitoring orshort-term diagnosis of performance. Permanently mounted sensors areleft in place for long periods of time and used for monitoring duringoperation or for convenient examinations. The sensors are typicallymounted in difficult-to-access locations with cables routed to easyaccess locations. On-board electronic instrumentation may be used forcontinuous monitoring while off-board portable electronics canoccasionally be plugged into the cables to obtain the sense elementresponses. In contrast, for short-term diagnosis, the sensors aremounted in a temporary fashion, such as with a weak bond or adhesivematerial, and on-board instrumentation is used to record data for shortperiods of vehicle operation, such as during a flight of a rotary wingaircraft. This allows the condition of the vehicle to be monitored fordiagnostic purposes, but the sensors and instrumentation can be removedand even reused on another vehicle.

Also, in operation, the calibration of the sensors can be performed in avariety of ways. For sensors that have a response which can beaccurately modeled, for example with the measurement grids of FIG. 11and FIG. 12, measurements of the sensor response in air may besufficient to adjust the instrument settings so that reliable propertymeasurements can be obtained. Alternatively, one or more measurementswith the sensor against a reference material can be used to make theseinstrument adjustments. The material properties determined by thesensors can in turn be related to the stress or strain through couponmeasurements. This relation can be obtained by applying a prescribedload to a coupon with one or more sensors mounted on the coupon.Alternatively, the relation could be obtained from controlled loadsapplied to a component resembling the application of interest, with oneor more of the sensors mounted to it. In both cases, a strain gage canbe mounted temporarily on the test material during loading to provide alocal measurement of strain to build correlation tables between themeasured electrical property (such as magnetic permeability orelectrical conductivity) and strain. In one embodiment, a cylindricalelement is loaded using pure torque loading, with appropriate straingages, pure tension loading, with appropriate strain gages, or axialloading, as well as combinations of these. In another embodiment thebending and axial stress are first estimated and then subtracted from acomplex loading mode to estimate pure torque stress. It follows thatthese pure torque stresses then have a direction of zero load (e.g.,axial) where, in-turn, a material property can be estimated independentof the complex loading modes and used to enhance the measurements. Forexample, the electrical conductivity could be estimated in the zero loaddirection for the pure torque stress and then used to correct fortemperature variations. While the above discussion emphasized therelation between a material property and the stress, strain, and load,empirical relationships between the sensor response and the state ofinterest can be stored to convert the sensor output to the desired statemeasurement for each sensor. Note also that thermocouples can be addedto the measurement system to enable correction for temperaturevariations.

FIG. 14 illustrates an example configuration for non-contact torquemeasurements on a rotorcraft. The quadridirectional sensors of FIG. 3and FIG. 4 are located on the inner surface of the inserts 52 so thatthe sensor is 0.050 inches from the surface of the rotating shaft 50.The insert 52 sits within a cylindrical sleeve 54 with non-conductingsupports behind the sensor that in turn is located on the top of thegearbox. By monitoring the shaft, the output torque from the gearbox canbe obtained. FIG. 15 shows a top view of this configuration. The sensorsin this configuration are reusable and also permit monitoring ofproperties through coatings. Similar applications are measurements ofthe torque on tool bits, stress measurement for bridge steels, and loadsin composites, such as those where the layout of the composite includes0°/90° and 45°/−45° plies.

In operation, each quadridirectional sensor can provide a measurement ofthe stress-dependent magnetic permeability of the shaft in fourdirections, as well as an estimate of the stress-independent electricalconductivity and sensor lift-off. This can be used to correct fortemperature variations. For example, a conductivity functionaldependence can be assumed or determined empirically for the testmaterial. Measurements of the temperature and conductivity at a nominalload can be used to establish a baseline value for the functionaldependence. Then, measurements at a different temperature can be used todetermine or validate the functional dependence. Note that thetemperature is the parameter of interest, not the conductivity, which ismeasured directly. The correction associated with the temperature canthen be used to adjust the sensor responses to provide atemperature-compensated value for each magnetic permeability. Note alsothat multiple frequency excitations can be used to measure propertyprofiles or spatial variations in properties with depth into the testmaterial.

Non-contact monitoring with a multi-directional sensor allows thelift-off (sensor proximity to the material surface) to provideadditional information about the operation of a component. For example,consider a multi-directional sensor placed proximate to a rotatingshaft. By measuring the lift-off at several positions around thecircumference of the shaft, any deflections in the shaft can be used tocalculate the bending modes and other loads on the shaft. The lift-offmeasurements could be used to correct or calibrate magnetic stress gagemeasurements or the torque measurements.

As an illustration, consider a torque measurement example for acylindrical shaft. This shaft represents a wide variety of applications,such as the rotor of a helicopter or a tool used in a machining ordrilling operation. Monitoring of the torque, for example, permitsreal-time force monitoring and control. Other parameters only need to bedetermined to the extent that they affect the parameter of interest(torque). In this case, the temperature of the shaft only needs to beknown to the extent necessary to remove any temperature dependence onthe material properties used to assess the torque, such as the magneticpermeability. The absolute value of temperature is not important andcould be, for example, offset by a constant value without directlyaffecting the robustness of the measurement. Fortunately, when multiplematerial properties are being determined in a measurement, such as themagnetic permeability and electrical conductivity, the property that isrelatively insensitive to stress, such as the electrical conductivity,can be used to estimate the temperature, while the stress dependentproperty, such as the magnetic permeability, can be used to determinethe torque. Similarly, since the torque should be the same around theshaft, the torque measurement can be assumed to be an average of thetorque measurements at each location. However, the bending stresses willbe zero if averaged around the circumference, so approximate correctionsfor bending should be sufficient to determine torque. Lift-off can bethe parameter used to estimate the bending stresses. When a shaft issubjected to bending modes, a deflection will occur that can be measuredby the lift-off of each sensor. Given a predefined relationship betweenbending stress and shaft deflection, either empirically or analyticallyderived, the bending stresses can be estimated based on shaftdeflection.

FIG. 16 shows a cross-sectional view of a shaft offset within a housing.In this implementation, nine sense elements are being used to estimatethe shaft offset based on lift-off. Permeability is being estimated atthe same nine locations in four orientations using a sensor such as thatshown in FIG. 4. The electrical conductivity is typically a linearfunction of temperature and can be assumed to change uniformly withtemperature for all locations and orientations.

Note that shaft velocity and angular position will be important if thematerial properties of the shaft vary significantly with angularposition. In this case, a signature can be developed of the permeabilityvariation of the shaft with position. This signature can be used tocompensate for the variation after load is applied. If no angularposition data is available, then a sense element in the no-loaddirection can be used to track the permeability changes, which can thembe compared to the signature to give shaft velocity and angularposition. This direction can also be used to compensate for temperatureeffects. Since the permeability should have a known and fixed value, anychanges in the measured properties should be due to temperature causinga conductivity change in the material. This information can be used tocorrect the measurements at other locations and orientations for thechange in temperature.

Several example measurements have been performed to demonstrate theoperation of the multi-directional sensors. For example, consider thequadridirectional sensor array of FIG. 5 with one pair of drive windingsexcited. For the sensors in locations 1 and 3 the excited drivecorresponds to the 0° and 90° orientations while for location 2 theexcited drive corresponds to the −45° and 45° orientations. Table 1shows the raw measured signal magnitude of the channels when one pair ofcomplementary orthogonal primary windings is excited. Each channelcorresponds to one group of sense elements associated with a primarywinding direction. This clearly shows that the sense elements respondprimarily to the associated excited primary windings of interest andthere is minimal cross-talk from the non-associated primary windings.

TABLE 1 Sense element responses when one pair of orthogonal drivewindings is excited. Location 0° 90° 45° −45° Location 1 0.966 1.0250.031 0.016 (Channels 1-4) Location 2 0.007 0.026 0.886 0.796 (Channels5-8) Location 3 0.946 0.928 0.037 0.002 (Channels 9-12)

In another example set of measurements, the magnetic permeability of asteel was monitored with the sensor array of FIG. 5 as the steel wasmechanically loaded. In this case, the sensor array was positioned neara magnetizable steel test material of thickness 0.061 in. and nominalelectrical conductivity of 2.5% IACS, with a lift-off of approximately0.030 in. An air calibration was performed and the data for each senseelement was processed using a magnetic permeability/lift-off measurementgrid. FIG. 17 shows the magnetic permeability and FIG. 18 shows thelift-off variation with stress, as the steel sample was bent. Themagnetic permeability changed for the sense element directionsappropriate for the stress variation while the estimated lift-off wasessentially constant. More specifically, Chan. 3, whose direction ofsensitivity to magnetic permeability was aligned with the direction ofapplied stress, showed the greatest change, while Chan. 4, which wasoriented at 90° to it, changed the least, and the remaining twochannels, which were at ±45° to the applied stress changed by similaramounts, of lesser magnitude than Chan. 3. The differences in lift-offbetween each sense element direction or measurement channel isconsistent with the sense elements being at different layers in thesensor stack-up. Similar results were obtained when the sensor directionwas rotated by 45°, as shown in FIG. 19 for the magnetic permeabilityand FIG. 20 for the lift-off variation, except that the roles of thesense elements were appropriately reordered, while the lift-offsremained unchanged.

As another example, measurements were performed with the sensor array ofFIG. 5 placed around a magnetizable steel shaft while it wasmechanically loaded in pure torsion. The shaft had an outside diameterof 2.0 in. and a 0.080-in. wall thickness. The shaft was supported in alathe and torque was applied using a 48-in. level arm with weights of350 lbs applied at radial distances of 24, 30, and 36 in. with respectto the shaft axis. Measurements were taken at three locations with foursense elements at each location, using the quadridirectional sensorarray shown in FIG. 5. One sensor was located at the top of the shaft,while the other two were placed ±120° away. The four sense elements ateach location were oriented to be sensitive to magnetic permeabilityvariations along the shaft axis (0°), perpendicular to the shaft axis(90°), and at −45° and 45° orientations to the axis. In this particulartest, only pure torsion was applied to the shaft. Consequently, theprincipal stresses occur at ±45° with respect to the shaft axis.

FIGS. 21 and 22 show the sensor response with applied torque. Thestresses in the shaft are zero for the 0° and 90° relative to the shaftaxis (channels 3 and 4) and are equal but opposite in the ±45°orientations (channels 1 and 2). These measured changes in the magneticpermeability correspond directly to the maximum and minimum stressdirections. Similar results were obtained for the other two sensors,verifying the capability of the sensors to monitor multi-directionalmaterial property variations without removing and replacing the sensornear the test material surface.

As an example illustrating the hysteresis correction, consider thepermeability-stress relationship that was measured on a flat steelspecimen in a bending fixture. Two MWM-Arrays were placed at rightangles, the first measuring the permeability in the axial direction andthe second in the transverse direction. Two conventional strain gageswere also installed on the specimen, measuring the strain in the sametwo orientations.

FIG. 23 shows the permeability versus stress relation over two stresscycles while FIG. 24 shows the result of applying a simple subtractionoperation to eliminate the hysteresis. As seen in the figure, the dataspread in the permeability/stress relationship due to hysteresis wasreduced significantly, from 0.7 to 0.18 (from 8.1% to 3.6% of the totalpermeability range). In this simple correction, information from onlyone other direction was used for the correction. In contrast with thesensor of FIG. 5, the second direction was not at the same location.Material variation from location to location contributes to noise andleads to a less-than-ideal correction for the hysteresis. The same setupdemonstrated the temperature dependence of the permeabilitymeasurements. Measurements were taken over the same stress range, atseveral different temperatures, as shown in FIG. 25. These resultsindicate that the slope and loop shape do not substantially change withtemperature. Normalization of these curves, for example by subtractingoff the average zero stress permeability, also shows the similarity ofthese curves.

To support refinement of the QD-MSG, a simple static test stand wasdesigned and fabricated. This test stand supported application oftorsion and bending loads simultaneously to create multi-dimensionalstress states typical of rotor shaft loading. On this test stand,several QD-MSGs were wrapped around the circumference of a hollow shaftthat is representative of an actual rotor shaft. A 0.060 in. thickplastic was placed between the sensors and the shaft as a representativedistance for implementation of a non-contact torque measurement onrotorcraft. Since these magnetic field sensors are not sensitive to thepresence of the plastic, this plastic provided a simple means ofsimulating an air gap between the sensor and the shaft. Eight straingages were also located near one of the three QD-MSGs. As describedabove, a solid mechanics model was used to convert the stresses at thelocation of each QD-MSG from the strain gage information. These stresseswere used to verify the system performance and establish the correlationbetween magnetic permeability and stress.

Using the static test stand, a data-processing methodology forconverting impedance measurements from the four channels in a QD-MSG todirectional stress estimates was developed. It is illustrated in FIG. 26and described as:

First, each of the four MWM sensors in a QD-MSG is calibratedsimultaneously using an air/shunt calibration 81. This calibrationcorrects for variations in cable, electronics and sensor behavior ateach sensor channel. A measurement grid (precomputed database) thatconverts the MWM response into permeability covers a range in theimpedance (real/imaginary) space. The air calibration brings theresponse of each MWM close to the correct operating point. The next step83 is a reference part recalibration that uses two measurements at twodifferent lift-offs (proximities). This calibration refinement uses afirst measurement at a lift-off different than the sensor nominalanticipated operating point and a second measurement at the nominaloperating lift-off. It is assumed that the only change between the twomeasurements is in lift-off. This is important and care must be taken inrecording these two points. The installation setup of the QD-MSG mustprovide a means by which to take these two measurements reliably. Fromthe MWM measurements at two lift-offs, an angle is determined betweenthe direction of the lift-off induced response change on the measurementgrid and the direction of the “lift-off” lines in the grid near theoperating point. MWM data is then rotated by this angle, using themeasurement at the nominal lift-off as the point about which to rotatenew data. Note that the static fixture prevents ideal performance ofthis calibration refinement since it requires unmounting and remountingthe sensor which introduces noise into the system.

Although not required, the calibration can be improved with a dynamiccalibration step. A significant noise source in the measurements and themain source of instrument drift is temperature dependence. Instrumentdrift is monitored through the use of an “air tip” (i.e., a QD-MSGmounted at a stable location in air, to be used as a reference). Bymonitoring how the measured air point fluctuates, the overall drift andtemperature response of the instrument can be characterized andcorrected. By removing drift and temperature effects due to theinstrument beforehand, the larger temperature effect, materialelectrical property variation with temperature, can be properlycorrected later.

The second step of processing the QD-MSG data, after each individualchannel has been properly calibrated, is the hysteresis correction 85.The hysteresis correction used on the above data requires a loading rampto obtain the hysteresis correction values which correlate permeabilitychanges in the insensitive direction (the insensitive direction is the90° direction, i.e., permeability measurement in the direction along thecircumference of the shaft) with permeability changes in the other threedirections (0°, +45°, −45°) at the same sensor location. A hysteresiscorrection ramp can be any ramp that starts with a no-load condition andrecords data at several loading conditions on the way up to a high load,and the same loading conditions on the way down.

After recording the hysteresis ramp data, an optimization method is usedto determine the factors that most accurately correlate the response ofthe channels with the insensitive orientation to the responses of theother channels 87. It is important to note that this is an initialhysteresis correction, in that it makes the assumption that the loadingconditions on the ramp down can be accurately matched to the loadingconditions on the ramp up. In the simple static setup, even “puretorque” cases can have a significant amount of bending and it is verydifficult to reach the same loading conditions on the way down as on theway up. Nevertheless, this initial hysteresis correction for the statictests worked reasonably well.

Using a bending ramp, as opposed to a torque ramp, lowers the resultingnoise by providing a better hysteresis correction because it is easierto recreate loading conditions in a pure bending scenario than the“pure” torque case in a simple static simple fixture. This led to animproved hysteresis correction that does not require such strict controlof the loading ramps. Preliminary tests of this new correction showimprovements when dealing with multiple applied loads.

The third step of processing is correcting for material temperatureeffects. Complicating matters, the permeability of the shaft beingmeasured is also temperature dependent 89. This can be corrected by ano-load normalization. This is a normalization of the permeability bythe most recently measured (or estimated) no-load point. As the materialtemperature drifts, the no-load response will vary slightly; thus,updating this no-load point is one way to remove temperature effects andenhance performance over long periods of time. From the physical model,it is possible to estimate how the no-load point changes by monitoringthe relative changes of the channels in different directions. Knowingthat torque will cause the two ±45° channels to move in equal andopposite directions and bending will affect the ±45° channels half asmuch as the 0° channel, with all three moving in the same direction, thedrift of the no-load point can be estimated asΔ_(no load)−(Δ₍₊₎₄₅+Δ⁽⁻⁾⁴⁵Δ₀)/2

where Δ denotes the change in each orientation. A change in shafttemperature manifests itself as a change in the no-load point. Bycorrelating the movement of the no-load point with the movement of thestress estimation of each channel, the no-load re-estimation methodeffectively compensates for temperature fluctuations 91.

The final (fourth) step of processing is multiplication by apermeability-to-stress factor 93. This factor is found by fitting acalibration set of data (i.e., the hysteresis ramp data after hysteresiscorrection similar to the data shown in FIG. 27) to the known loads, asdetermined by the strain gages during initial calibration of the QD-MSG,applied in order to convert from permeability response to stress.Research to date has shown this factor to be portable and timeinvariant. The permeability-to-stress relationship appears to be asimple linear relationship. This dramatically simplifies implementationand should enable convenient implementation of control algorithms andother uses for this non-contact torque data.

FIG. 27 shows the successful implementation of the above method. Threeof the QD-MSG channels, which are in three different orientations(axial, i.e. 0°, 45°, and −45°) are plotted against the stresses,derived from the strain gages using a solid-mechanics model, acting inthe direction in which the channel measures permeability. For an MWMsensor, and for each QD-MSG channel, this direction is perpendicular tothe longer drive winding segments. The same results were obtained frommultiple tests. Data taken on different days share the same hysteresiscorrection factors and the same initial calibration. A no-loadrecalibration is then performed, without modification to the hysteresiscorrection factors. The responses are shown for varying applied stresses(as measured by the strain gages). The fourth channel at the 90°orientation was used for hysteresis correction, as described earlier.The stresses are applied by a combination of torsion and bending in thesimple static test setup. Many different combinations of torsion andbending loads were applied to create a variety of multi-directionalstress states. A portion of the data from the first test was used as acalibration set to develop the hysteresis correction factors. The linearcorrelation was obtained for both bi-directional and uni-directionalloading schemes.

The successful implementation of the temperature correction was alsoexamined in the simple static test setup. FIG. 28 shows the QD-MSGresponse before the no-load estimation temperature correction. Thisshows that a 20 degree temperature shift can have a significant effecton the measurement response. However, after the temperature correctionthe results are equivalent to FIG. 27.

The algorithm and procedures developed using the simple static testsetup was then applied to two full-scale dynamic tests. Theconfiguration selected for these dynamic tests used nine QD-MSGs equallyspaced around the circumference of the helicopter rotor shaft. Threesensor strips, each with three QD-MSGs and each covering ⅓ of the fullcircumference of the shaft, were installed. In each of the QD-MSGs, themagnetic permeability, and thus the stress, were measured in fourdirections: 0°, 90°, 45°, and −45°. The stresses at all nine locations(three sensor strips with three QD-MSGs each) were used to determine thetorque, bending, and axial loads. Also, each sensor provides anindependent lift-off (proximity) measurement. This proximity measurementcan be used to refine load estimates (i.e., to identify bending loaddirection) or to provide an independent measure of radial vibrations.

The test facility had the capability to apply torque, bending, axial,and drag loads. The torque was applied by means of a closed-loopmechanical feedback system. The bending, axial, and drag loads wereapplied by hydraulic actuators. The magnitudes of the applied forceswere monitored via load cells attached to the hydraulic actuators. Thegoal of these tests was both to enable the demonstration of non-contacttorque sensing in a realistic environment.

In the first dynamic test, the ability to estimate torque in the puretorque case was assessed, as well as the robustness of the calibrationand hysteresis correction methods. With the sensor assembly mounted ontoa gearbox and the gearbox mounted into the test stand, the setup was runat full speed under a variety of loading conditions. These conditionsincluded torques from 20% to 100% of the maximum design torque, as wellas various levels of bending loads and lifting loads. FIG. 29 showsmeasured permeability data after temperature correction but prior tohysteresis correction for each of the four MWM channels in one of theQD-MSGs. This data is typical of a hysteresis correction ramp. FIG. 30shows the effect of hysteresis correction on the dynamic test data. Theresult of the procedure developed on the simple static test stand,described above, is an essentially linear relationship between thehysteresis-corrected MWM permeability measurements and the stresses inthe rotor shaft, which was derived from strain gages installed on theshaft. The dynamic test results appear far less noisy, because theloading controls on the dynamic test setup are much better than on thesimple static test facility, the strain gage data is more reliable, andthe lift-off can be adjusted for calibration without removal of thesensors. The same results for FIG. 30 were observed at later times anddays, which demonstrated the robustness of the calibration methods. Thisis critical for final implementation. For example, one can load a shaftduring initial installation in production. Then the hysteresiscorrection loading ramp and the permeability-to-stress relationship forthat individual shaft would be stored and reused over the life of therotorcraft, or at least until the next major maintenance opportunity.

In a second full-scale dynamic test, the no-load normalization wasimplemented as part of the calibration procedure. From the bendingstrain gage data, it was apparent that the intended “pure torque” casesdid have some bending load contamination. Applying a torque whilespinning at 225 rpm resulted in an unintended bending load that wasabout 20% of the maximum bending load used in the pure bending tests.Independently, by observing the deflection of the shaft through changesin lift-off measurements, it became clear that the nominal bending dueto torque was in a different direction than the bending load due to ahub moment. If the shaft were to deflect in a given direction, one wouldexpect the change in lift-off to be sinusoidal with position around theshaft, with the maximum being the direction of bending. As can be seenin FIG. 31, which plots the QD-MSG-measured lift-off (displacement fromthe average), the peaks of the sinusoidal liftoff-displacement curve arein two different angles, depending on whether the bending is purposelyapplied or an artifact of the intended torque application.

This plot is significant as it highlights a drawback to the originalhysteresis correction method which required a loading ramp withpredetermined pure loading states. It is unreasonable to assume thatpure torque can be applied, and such an assumption would result in aninaccurate hysteresis correction. Furthermore, this lift-off monitoringdemonstration is the first step in developing the capability to monitorshaft vibrations.

Using this data as a reference, the hysteresis correction procedure wasenhanced to work with generic, multi-axial loading. The fundamentaldifference between the original hysteresis correction and the new, moregeneral hysteresis correction is the assumption that is made tocalculate the factors. In the original method, pure, known loadingstates were assumed and a linear relationship was discovered. In the newmethod, a linear relationship is assumed, and strain gauge data is usedto identify what the loading states are on the calibration loading ramp.This provides enough information to determine the hysteresis correctionfactors regardless of the complexity of the loading state. Anotheradvantage is that this new method simultaneously calculates thepermeability-stress factors. FIG. 32 and FIG. 33 show the effect of thisnew calibration procedure. FIG. 32 shows a sample set of data correctedfor hysteresis using the old calibration procedure. FIG. 33 shows thesame data as FIG. 32, but calibrated using the new multi-axial loadingprocedure. This procedure allows a full range of loads to be applied tothe shaft during the hysteresis correction. As long as the loads areknown, the hysteresis correction can be calibrated to produce a linearresponse. This substantially reduces the rigor required to control theloads for proper sensor calibration and hysteresis correction, makingthis solution more practical.

FIG. 34 shows the final torque estimates based on the QD-MSG data versusestimated applied torque. Several of the data sets included in this plothave applied bending loads. The response is linear and the error is low.

FIG. 31 also demonstrates other measurement capabilities. Changes in thelift-off monitored over time and at multiple circumferential locationscan be used to approximate bending loads. This provides a means checkthe magnetic property variation estimate of the bending load for errors.Furthermore, this information can be used to determine the direction ofbending and provides perspective on the current dynamic mode for theoperation of the shaft.

The above algorithm for calculating shaft loads giving multi-directionalpermeability measurements makes one assumption; the stress in theno-load direction is effectively zero. This, however, is only accurateif the hoop stress due to the rotation of the shaft is small. Given alarge hoop-stress, another correction would be needed. With anestimation of the shaft rotation rate (e.g., from an encoder or shaftmaterial variations) and knowledge of the shaft geometry and materialproperties, the hoop stress can be calculated and corrected for.

Another application is dynamic stress assessment of a rotating componentcontaining discrete feature, such as individual posts or planets isdescribed in while U.S. patent application Ser. No. 11/702,422 titled“Quasistatic Magnetic and Electric Field Stress/Strain Gages,” filedFeb. 5, 2007, the entire teachings of which are incorporated herein byreference. Here, the approach is extended by providing for the use ofnoncontact measurements that can be used to assess the torque on therotating component. Furthermore, the stress or torque of the individualfeatures is used to obtain the net torque on the system, such as on therotor shaft. The information from the measurements on each post can beused as part of a condition based maintenance program for the component.Note that this approach can also be used to measure features of objectsmoving relative to the stationary member. Examples include the weight oftrucks on a bridge and the effect of wind on a bridge or similarstructure.

For example, four MWM sensors (or magnetic stress gages) were mountedaround the outer, accessible circumference of a ring gear. Theprotective coating on the outside of the ring gear was left intact andnot removed for the sensor installation. The magnetic permeability ateach of these locations was then estimated using a multivariate inversemethod. The permeability versus stress relationship for this materialwas then determined. During operation, the local stress estimates fromeach sensor were converted into estimate of the stress on the individualcarrier plate posts using a using a systems identification approach. Theindividual post stresses were then combined into a torque estimate forthe main rotor shaft as shown in FIG. 35. Variations in these signalsthen allow the remaining life for individual carrier plates to bedetermined, to determine if geometric anomalies or other factors arecausing overloading or higher loads than anticipated, and as input forremaining life estimation of other dynamic components.

Note also that these sensors and measurement methods can be applied toother material systems, such as composite structures. As an example,consider FIG. 36, where a sensor having a a drive winding 10 is placedover a composite test material 68. The sense elements 64 provide aresponse that can be related to the composite material conditiondepending upon the applied loads, such as mechanical or thermal appliedloads. For example, the temperature of the test material can also bevaried with ambient conditions or sources 62 such as heat lamps orlasers typical of other thermal nondestructive inspection methods asdescribed in U.S. patent application Ser. No. 11/036,780, filed Jan. 14,2005, the entire teachings of which are incorporated herein byreference. Using one or more thermal sense elements 66 (or strain gagesfor mechanical loading) placed in the vicinity of the drive windingsense the temperature of the test material. These thermal sense elementscan be thermistors, thermocouples, or other temperature sensitivedevices. The drive windings can be oriented in specific directions withrespect to the fibers of the composite to enhance sensitivity to thecondition of interest, such as the temperature or stress. When sensorswith multiple drive windings are selected, the angle between the drivewindings, or the angle between the magnetic field directions associatedwith each drive winding orientation, can be selected to match the fiberorientation in the difference plies or laminates of the compositestructure. For such heterogeneous materials, it is often convenient toexpress the effective or composite properties in terms of a complexdiamagnetic permeability, as described for example in U.S. Pat. No.5,453,689.

In many situations, the sensor or sensor array will be in motionrelative to the test material. This can occur, for example, whenscanning across the surface of a material for a flaw. Most often thetime interval determined by the scanning speed and the characteristiclength scale of the sensor is much greater than the time period of theimposed AC field, in which case the effects of the motion arenegligible. As described for example in U.S. Pat. No. 6,992,482, in somesituations the relative motion of the sensor and the material under testcan influence the magnetic field distribution and the sensor response.For example, for a spatially periodic winding distribution and materialmotion in the same direction, then the magnetic vector decaysexponentially with distance into a uniform material with a decay rateγ=√{square root over (k² +jσμ(ω31 ku))}

where k=2π/λ is the wavenumber, σ is the electrical conductivity, μ isthe permeability, ω=2πf is the angular frequency of the excitation, andμ is the material velocity. The velocity has the effect of changing theeffective frequency of the excitation and hence the decay rate of themagnetic field into the material under test. This effect can be modeledand FIG. 37 shows how the depth of penetration of the magnetic field(expressed as 1/Re(γ) varies with the excitation frequency of the drivecurrent and the rotation rate of a cylindrical shaft. In this case,assumed nominal values were a spatial wavelength of 0.02 m, relativepermeability of 15, conductivity of 2% IACS, outside diameter of 0.092m, and rotation rate of 225 rpm. For low rotation rates, the depth ofpenetration is not affected by the movement of the test material.However, at relatively high rotation rates and relatively low excitationfrequencies, there can be a significant effect of the material motion onthe depth of penetration of the magnetic field and on the resultingsensor response.

While the inventions have been particularly shown and described withreference to preferred embodiments thereof, it will be understood tothose skilled in the art that various changes in form and details may bemade therein without departing from the spirit and scope of theinvention as defined by the appended claims.

What is claimed is:
 1. A method for stress assessment comprising:disposing a sensor proximate to a test material, the sensor having atleast two drive windings and at least two sense elements, the drivewindings connected in series for exciting a spatially periodic magneticfield of at least two periods when driven by an electric current, withthe drive windings oriented in at least two different directions,positioned in at least two separate planes, and covering an overlappingarea of the test material, the sense elements sensing a response to thetest material, with each sense element positioned to measure a testmaterial response primarily associated with one of the drive windingsand not with the other drive windings; converting the response of eachsense element into a property estimate for the test material in at leasttwo directions, the property estimate exhibiting hysteresis as anapplied load varies the stress of the test material; and correlating aproperty estimate to the stress of the test material in a firstdirection, with a property estimate in at least one second directionused to remove hysteresis effects on the property estimate in the firstdirection, the hysteresis effect determined by loading the test materialto a known level and computing at least one correction factor thatremoves the hysteresis from the first direction.
 2. The method asclaimed in claim 1 further comprising: the test material being arotating cylinder; the sensor having two pairs of orthogonal drivewindings and sense elements, stationary, not in contact with the testmaterial; and the stress providing a measured load on the rotatingcylinder.
 3. The method as claimed in claim 2 wherein the measured loadis the torque on the rotating cylinder.
 4. The method as claimed inclaim 2 wherein the measured load is an axial load on the rotatingcylinder.
 5. The method as claimed in claim 2 wherein the measured loadis a bending load on the rotating cylinder.
 6. The method as claimed inclaim 1 wherein the stress in at least two directions is determined fromat least three drive windings and at least three sense elements.
 7. Themethod as claimed in claim 1 wherein the stress provides a measure oftorque, bending and axial load on a spinning shaft in a drive system. 8.The method as claimed in claim 1 wherein the stress is measured in atleast two directions on a ferrous metal structural member or astructural member coated with a ferrous metal, and the property is amagnetic permeability.
 9. The method as claimed in claim 1 whereinsensing element measurements are made simultaneously.